Question

What is timelike separation in special relativity? What is spacelike separation?

Answer 1

Imagine that we have two points with coordinates $A(ct_1, x_1), B(ct_2, x_2).$ What is the distance between them? The answer is

$$s^2=c^2(t_2-t_1)^2-(x_2-x_1)^2.$$

The separation is timelike if $s^2>0.$

The separation is spacelike if $s^2<0.$